UV Unwrapping makes a mess and misses faces
You simply need to mark all the seems correctly and it will umwrap nicely. Make sure you mark all the small edges that could interfere with the unwrapping and try again.
Use ctrl+e while in edit mode to call the Edge menu where you can find Mark Seam.

It is also a good idea to apply scale of the object to get expected results when unwrapping. You can do that with ctrl+a with the object selected in object mode: